Following [1]}'s development, there are many extensions under more relaxed settings. The result in [1]} was generalized by [3]} by removing the constraint on the fourth moment of the underlying random variables. After that [4]} showed that the CLT of LSS for non-centered sample covariance matrices and [5]} studied the unbiased sample covariance matrix when the population mean is unknown with general moment conditions. [6]} focused on the ultra-high dimensional case when the dimension \(p\)  is much larger than the sample size \(n\) . Other extensions on this topic can be found in [7]}, [8]}, [9]}, [10]}, and so on.
